Just to get an intuitive feel about the force. I came up with a imaginary situation of a long aisle on a huge rotating disk, like a groove along the diameter of a disk.
Now as this disk starts rotating if you were standing somewhere in the aisle it would push you outwards from the centre. As you move outwards your tangential velocity will have to increase and hence enact a acceleration upon you thus a force. This force which causes your tangential speed along the perpendicular to radius to increase is the Coriolis force.
Is my explanation correct, if not would someone mind giving a scenario apt for visualizing the force.